{"paper":{"title":"The Essential Spectrum of Toeplitz Operators on the Unit Ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Raffael Hagger","submitted_at":"2017-05-12T13:08:30Z","abstract_excerpt":"In this paper we study the Fredholm properties of Toeplitz operators acting on weighted Bergman spaces $A^p_{\\nu}(\\mathbb{B}^n)$, where $p \\in (1,\\infty)$ and $\\mathbb{B}^n \\subset \\mathbb{C}^n$ denotes the $n$-dimensional open unit ball. Let $f$ be a continuous function on the Euclidean closure of $\\mathbb{B}^n$. It is well-known that then the corresponding Toeplitz operator $T_f$ is Fredholm if and only if $f$ has no zeros on the boundary $\\partial\\mathbb{B}^n$. As a consequence, the essential spectrum of $T_f$ is given by the boundary values of $f$. We extend this result to all operators in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04553","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}